Trevor
What I am describing is not a mystical experience and has nothing to do with spirituality, belief or prayer. It is simply the understanding that being asleep or awake and thinking are not the only two gears the mind has.
There are other of states of mind. Hypnosis shows how easily the thinking mind can be altered by digging a little below the surface. Thinking is a most important tool but it can also cause neurosis and other anxiety problems when a person has not learned to control the intensity of the thought process.
I can identify with the above - its simple straightforward and works.
As a dub I stumbled across what you have described via Alexander Technique. It taught me to adopt a neutral frame of mind of non -doing and non thinking. This state was acceptable to me as a witness and very helpful to go into for about 15-20 minutes a day. For me it was more calming than prayer - I'd feel stable and happy once again. Able to face the world. I still use it - it has become a part of my life.